1. **State the problem:** We need to determine which fraction is greater: $-\frac{55}{33}$ or $-\frac{24}{33}$. 2. **Understand the fractions:** Both fractions have the same denominator, 33, and both are negative. 3. **Rule for comparing fractions with the same denominator:** When denominators are the same, the fraction with the larger numerator is greater if both are positive. For negative fractions, the one with the smaller absolute numerator is greater because it is less negative. 4. **Compare the numerators:** $55$ and $24$. 5. **Since both fractions are negative, $-\frac{24}{33}$ is greater than $-\frac{55}{33}$ because $24 < 55$ and less negative means greater. 6. **Final answer:** $-\frac{24}{33} > -\frac{55}{33}$.